Abstract

Splitting methods have been playing an important role in approximating solutions of numerous modeling problems including those in the ice sheet dynamics. Of course, splitting methods are not limited for solutions of differential equations. They are also used in statistical computations and optimization. The modern ideas of splitting can be traced back to Henry F. Baker (1866-1956), John E. Campbell (1862-1924) and Felix Hausdorff (1868-1942). The strategies have been booming since the arrival of the first electronic computer. A splitting method separates a sophisticated mathematical model into several subproblems, separately computes the solution to each of them, and then combines all sub-solutions to form an approximation of the solution to the original problem. A canonical example is splitting of waves of different frequencies in a general wave partial differential equation. The splitting idea generalizes in a natural way to problems with multiple operators too. In all cases, the computational advantage is that it is faster to compute the solution of the split components separately, than to compute the solution directly when they are treated together. However, this comes at the cost of an error introduced by the splitting, so strategies must be devised for controlling the error. This presentation recalls the phenomenal work done by the pioneers and introduces the methodology via modern operators. A short conversation will be given in global error analysis of popular exponential splitting formulations.

*This talk is suitable for all graduate students. It may also be good for junior, senior undergraduate students after learning the calculus.

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m927a9275472558919f5b9c1b58beb030